Iterative algorithms for solving generalized nonlinear mixed variational inequalities
Pages 399 - 408
Abstract
A new concept of g-partially relaxed strong monotonicity of mappings is introduced. By applying the auxiliary variational inequality technique, some new predictor-corrector iterative algorithms for solving generalized nonlinear mixed variational inequalities are suggested and analyzed. The convergence of the algorithms only need the continuity and the g-partially relaxed strongly monotonicity of mappings. These algorithms and convergence result are new, and generalize some known results in literature.
References
[1]
{1} J.P. Aubin, A. Cellina, Differential Inclusions, Springer, New York, 1984.
[2]
{2} K.C. Border, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, 1985.
[3]
{3} X.P. Ding, E. Tarafdar, Generalized nonlinear variational inequalities with nonmonotone set-valued mappings, Appl. Math. Lett. 7 (4) (1994) 5-11.
[4]
{4} X.P. Ding, E. Tarafdar, Existence and uniqueness of solutions for a general nonlinear variational inequality, Appl. Math. Lett. 8 (1) (1995) 31-36.
[5]
{5} X.P. Ding, Algorithm of solutions for mixed implicit quasivariational inequalities, Comput. Math. Appl. 38 (1999) 231-241.
[6]
{6} X.P. Ding, On generalized mixed variational-like inequalities, J. Sichuan Normal Univ. 22 (5) (1999) 494-503.
[7]
{7} R. Glowinski, J.L. Lions, R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, 1981.
[8]
{8} P.T. Harker, J.S. Pang, Finite dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications, Math. Programming 48 (1990) 161-220.
[9]
{9} P. Marcotte, L.H. Wu, On the convergence of projection methods: applications to decomposition of affine variational inequalities, J. Optim. Theory Appl. 85 (1995) 347-362.
[10]
{10} M.A. Noor, General algorithm for variational inequalities, J. Optim. Theory Appl. 73 (1992) 409-413.
[11]
{11} M.A. Noor, Auxiliary principle for generalized mixed variational-like inequalities, J. Math. Anal. Appl. 215 (1997) 75-85.
[12]
{12} M.A. Noor, A Class of new iterative methods for general mixed variational inequalities, Math. Comput. Modelling 31 (2000) 11-19.
[13]
{13} M.A. Noor, A predictor-corrector algorithm for general variational inequalities, Appl. Math. Lett. 14 (2001) 53-58.
[14]
{14} M.A. Noor, Solvability of multivalued general mixed variational inequalities, J. Math. Anal. Appl. 261 (2001) 390-402.
[15]
{15} M.A. Noor, Iterative methods for generalized variational inequalities, Appl. Math. Lett. 15 (1) (2002) 77-82.
[16]
{16} R.U. Verma, Partially relaxed monotone mappings and a system of nonlinear variational inequalities, Nonlinear Funct. Anal. Appl. 5 (1) (2000) 65-72.
[17]
{17} D.L. Zhu, P. Marcotte, An extended descent framework for variational inequalities, J. Optim. Theory Appl. 80 (1994) 349-366.
Index Terms
- Iterative algorithms for solving generalized nonlinear mixed variational inequalities
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Published: 01 December 2004
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